Dynamics of boson quantum films

We employ a quantitative microscopic theory of nonuniform quantum liquids to explore the excitations in thin films of He4 adsorbed onto a substrate. These liquid films studied undergo a series of structural phase transitions coinciding with the completion of individual atomic layers. A generalized Feynman ansatz is used for the wave function of the excited states; multiphonon effects are included by generalizing the Feynman theory to allow for time-dependent pair correlations. We study the dispersion relation, excitation mechanisms, transition densities, and particle currents, as a function of the surface coverage, including coverages near the phase transitions. Because of the film's layered growth, the sound velocity exhibits a series of minima and maxima. A pronounced long-wavelength softening of the lowest-energy mode is observed near the transitions. In the monolayer, the nature of the excitations undergoes a noticeable change at the coverage where the velocity of sound starts to decrease. This is a crossover from ''essentially two-dimensional'' to ''essentially three-dimensional'' behavior. At long wavelengths, below and above the crossover coverage, the lowest-energy excitation is a longitudinal phonon (propagating within the monolayer) and a surface excitation, respectively. At shorter wavelengths, a layer-phonon propagating within the liquid layers, level crosses with a surface excitation to become the lowest-energy mode. For double- and higher-layer films the excitations are complicated by multiple (layer phonon with layer phonon and layer phonon with surface excitation) level crossings. At higher coverages, a mode is identifiable that will evolve into the bulk phonon-maxon roton. Our results agree qualitatively with the available spectra obtained by neutron scattering experiments.